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abacus21 · Jun 1, 2010, 03:09 PM

Use the Maclaurin series of cos(x) to state the first three non zero terms of the Maclaurin Series for (1-cos x)/x^2

galactus · Jun 1, 2010, 06:43 PM

The series for cos(x) is

$\sum_{k=0}^{\infty}(-1)^{k}\frac{x^{2k}}{(2k+1)!}$

Just do as it says. Subtract from 1 and then divide that result by x^2.

This eliminates the 1 in the original series for cos(x), switches the signs, and reduces the powers of x in the numerators by a power of 2.

$\sum_{k=0}^{\infty}(-1)^{k}\frac{x^{2k}}{(2k+2)!}$